PDF Archive

Easily share your PDF documents with your contacts, on the Web and Social Networks.

Share a file Manage my documents Convert Recover PDF Search Help Contact



The Location Privacy Protection of Electric Vehicles with Differential Privacy in V2G Networks .pdf



Original filename: The Location Privacy Protection of Electric Vehicles with Differential Privacy in V2G Networks.pdf

This PDF 1.7 document has been generated by / iText® 7.1.1 ©2000-2018 iText Group NV (AGPL-version), and has been sent on pdf-archive.com on 01/10/2018 at 13:12, from IP address 193.137.x.x. The current document download page has been viewed 180 times.
File size: 3.9 MB (17 pages).
Privacy: public file




Download original PDF file









Document preview


energies
Article

The Location Privacy Protection of Electric Vehicles
with Differential Privacy in V2G Networks
Yuancheng Li 1, *, Pan Zhang 1,2 and Yimeng Wang 1
1
2

*

School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China;
pan-zhang@sgcc.com.cn (P.Z.); 1162227078@ncepu.edu.cn (Y.W.)
State Grid Information & Telecommunication Branch, Beijing 100761, China
Correspondence: yuancheng@ncepu.edu.cn

Received: 10 September 2018; Accepted: 28 September 2018; Published: 1 October 2018




Abstract: Vehicle-to-grid (V2G) is an important component of smart grids and plays a significant
role in improving grid stability, reducing energy consumption and generating cost. However, while
electric vehicles are being charged, it is possible to expose the location and movement trajectories
of the electric vehicles, thereby triggering a series of privacy and security issues. In response to this
problem, we propose a new quadtree-based spatial decomposition algorithm to protect the location
privacy of electric vehicles. First of all, we use a random sampling algorithm, which is based on
differential privacy, to obtain enough spatial data to achieve the balance between large-scale spatial
data and the amount of noise. Secondly, in order to overcome the shortcomings of using tree height
to control Laplacian noise in the quadtree, we use sparse vector technology to control the noise
added to the tree nodes. Finally, according to the vehicle-to-grid network structure in the smart grid,
we propose a location privacy protection model based on distributed differential privacy technology
for EVs in vehicle-to-grid networks. We demonstrate application of the proposed model in real spatial
data and show that it can achieve the best effect on the security of the algorithm and the availability
of data.
Keywords: electric vehicle (EV); location privacy protection; differential privacy; random sampling
algorithm; sparse vector technology; vehicle to grid (V2G)

1. Introduction
Vehicle-to-grid (V2G) is an important sub-system of smart grids. With the characteristics of electric
vehicles charging and discharging, a vehicle-to-grid network can help grid load to “peak-fill”, improve
grid stability, reduce energy consumption and reduce power generation cost [1]. Vehicle-to-networks
is also suitable for some small-scale energy management systems [2]. As we all know, the range of
charging pile locations can affect the degree of participation. In the case of high participation [3],
the total cost of the energy system will decrease [4], and electricity prices will fall [5]. However,
electric vehicle-to-grid accelerates transformer aging [6]. Therefore, vehicle-to-grid is a double-edged
sword [7]. At the same time, the V2G network has also introduced new privacy issues, such as the
user’s home address, place of work, place of entertainment, and places frequented, which may be
reflected in the charging history. Leaking location information has a negative impact on users, being
harassed by location-based spam, unscrupulous merchants selling location-related products or services
to users without permission [8]. In addition, the leaked location information may also expose the user’s
health status, religious beliefs, personal preferences, social relations and other private information [9].
For example, the stay period and frequency of visits of an electric car at a hospital may expose the
user’s health condition. More seriously, location information may also cause security problems, which
might be used by criminals, allowing users to be tracked, looted, and even suffer from personal
Energies 2018, 11, 2625; doi:10.3390/en11102625

www.mdpi.com/journal/energies

Energies 2018, 11, 2625

2 of 17

attacks [10]. Therefore, the privacy of EV location is very important to the normal operation of smart
grid, the safety of electric vehicle users and the popularization of electric vehicles. Therefore, it is
important to study the privacy protection of the EV location in vehicle-to-grid networks.
The control center of the power grid optimizes the charging and discharging of the electric vehicle
by monitoring the position of the electric vehicle. When performing location data query and access,
the spatial search tree or grid structure that meets the requirements is usually established based on
the spatial segmentation technique. There is a lot of research work based on the privacy protection
scheme proposed by the spatial segmentation technology, such as adding noise to the established
spatial search tree or network unit, and disturbing the location of the individual. As the degree of noise
is added, the privacy protection of individual locations is better, but the accuracy of search and query
is also reduced. At the same time, most privacy protection algorithms based on spatial segmentation
technology are mostly affected by data distribution. When the amount of data is relatively large, or the
data skew is serious, the accuracy and privacy protection effect of the algorithm are very limited.
Among the problems we studied, the amount of location data in the V2G network is huge, and the
original spatial segmentation algorithm does not have a good effect on accuracy and data availability.
Therefore, in this paper, we proposed a spatial data privacy protection algorithm for V2G networks,
adding noise that satisfies differential privacy in the spatial segmentation algorithm, ensuring the
security of individual location data while keeping data query and access with good precision.
In summary, we make the following contributions in this paper:
(1)
(2)

(3)
(4)

We propose a new random sampling algorithm based on differential privacy, which can obtain
enough samples to deal with large-scale spatial data.
We propose a new quadtree-based spatial decomposition algorithm, and use sparse vector
technology to control the depth of the tree to achieve independent tree-depth noise control and
better protect the privacy of the location data.
We propose the vehicle-to-grid location data protection model based on differential privacy to
realize the privacy protection of EVs locations in vehicle-to-grid networks.
We conduct experiments on actual EVs locations data to prove our proposed method and to
achieve the best effect on the security of algorithm and availability of data.

The rest of our paper is organized as follows: in Section 2 we introduce the related work of
privacy protection of vehicle-to-grid in a smart grid; in Section 3 we introduce the network structure of
vehicle-to-grid in a smart grid; in Section 4 we propose the spatial data decomposition method with
differential privacy; in Section 5 we implement experiments to verify the validity of the algorithm; and
in Section 6 we conclude our paper.
2. Related Work
In recent years, many researchers have proposed some protocols to protect the privacy of electric
vehicles. Based on the characteristics of vehicle-to-grid networks, Yang et al. first proposed the
privacy issue of electric vehicle users, and proposed a protection privacy communication with an
accurate reward system structure [11]. In this architecture, the user’s “permission” generated by the
ID-based restricted partially blind signature technology can access the V2G network anonymously,
so as to protect the user’s identity and location privacy. Each time the user sells electricity, he can
obtain the “reward” signature, and according to this “reward”, the corresponding reward can be
obtained anonymously. However, it has the problem of key escrow in this scheme [12], which
proposes a new scheme using the restricted partial blind signature technique under the setting of
certificate-free public key. Reference [13] protects the location privacy of charging users by constantly
changing their fake identities to ensure that electric vehicles can change different fake identities in
different parking lots. A secure electric vehicle payment system was proposed to support two-way
anonymous payment while still paying the right fee or getting paid [14]. Their scheme can guarantee
anonymity, while supporting the function of tracking, fraud prevention and arbitration. Reference [15]

Energies 2018, 11, 2625

3 of 17

analyzed the impact of honest but curious aggregators on the privacy of EV users and proposed
a model to prevent aggregators from tracking users by reducing the amount of data transferred.
Reference [16] studied the privacy problem when users use advanced measurement systems to
participate in vehicle-to-grid at home, and proposed the vehicle-to-grid architecture to hide the
user’s pseudo-identity information in K gateways to realize the privacy protection of user data. These
methods all use pseudo-identities [13–16] for privacy protection. In this paper, we proposed a location
privacy protection algorithm based on differential privacy. We obtained good effects only by processing
location data. Unlike pseudo-identities technology, we do not need extra computational overhead
when calculating pseudo-identities.
On the other hand, many researches on spatial decomposition technology are based on differential
privacy to protect the location of spatial data privacy. Spatial decomposition technology commonly
uses indexing technology, such as grid structure and tree structure. The HKD-tree proposed in
Reference [17] is an early representative of data-independent decomposition. This method divides
the data by grid and adds noise to each grid cell, which utilizes KD-tree for indexing. However,
this algorithm is valid only if the data distribution is balanced. The uniform-grid (UG) model in
Reference [18] uses a well-distributed grid to decompose two-dimensional spatial data and adds
noise to each of the cells. Although UG can be more reasonable to set the granularity of the division,
it does not consider skew and sparseness of data distribution. If a cell is especially sparse, even
a count of zero, it will result in excessive noise error; on the other hand, if a cell is especially dense,
it cannot be completely divided and will result in an excessive assumption error. The DP-where
method in Reference [19] also uses a well-distributed grid to decompose the working position and
family position of a moving crowd, but the disadvantages of this method are similar to that of UG.
For the lack of UG method, adaptive-grid (AG) model was proposed [18] according to the different
granularity of the high-level division unit, to divide the spatial data adaptively top-down. Although
AG can set the granularity of spatial data adaptively according to the data sparseness, it does not
give the corresponding heuristic rules to distinguish the boundaries between the dense and sparse
data. In addition, this method does not consider the actual distribution of the original data either.
Reference [20] proposed the AG method adapted for spatial decomposition, and then utilizing the
Laplace mechanism to protect the worker’s position information. A complete quadtree is used to
decompose the two-dimensional spatial data top-down in Reference [21]. The complete quadtree
needs to satisfy all leaf-to-root paths with the same length, and all intermediate nodes have the same
fan-out. In order to improve the decomposition accuracy, quadpost uses the geometric distribution
technology to divide the privacy cost and post-processes the noise by the least squares unbiased
estimation. The advantage of this method is that the privacy budget can be rationally distributed,
and the noise error is low. The disadvantage is that the depth of the tree is used to control the noise
value. If the depth of the tree is relatively large, the noise added in each layer is especially high.
Accordingly, the final query accuracy will be low. In addition, this method does not consider the
original data distribution, and the uniform hypothesis error is relatively high. Quadtree and Kalman
filtering were used to decompose dynamic spatial data in Reference [22]. It utilizes a heuristic threshold
to judge whether each partitioned unit is sparse or dense. If the unit is still dense, it will be partitioned
continually. The disadvantages of Reference [22] are similar to those of Reference [21], depending on
the depth of tree to control the noise value. Compared to the first two methods, [23] combined complete
quadtree to partition spatial data, responding to range queries by releasing leaf node noise counts and
non-leaf node domain information. This method does not rely on the tree depth. It reduces the noise
through the offset value of the node count, and then uses a noise constant to determine whether to
divide the node. Meanwhile, this method uses the sparse vector technique [24,25] to calculate the node
decomposition threshold. The b-ary tree is used to partition the data levelly in Reference [26]. The noise
is used to perturb the counts in each node, and the statistical information of each layer is published as
a histogram. However, this method also uses tree depth to control noise. Reference [27] uses b-ary
tree to decompose the data as well. The method discusses the relationship between tree depth, tree

Energies 2018, 11, 2625

4 of 17

fan-out and data dimension, and post-processes the query results. Reference [28] used the sampling
method to process the spatial data, and then divided the spatial counts into groups of the same size,
adding noise to the mean of each group. However, the final accuracy of the method was relatively low.
DP-tree method using embedded trees was proposed to decompose multi-dimensional spatial data
and supports range count queries [29]. However, this method uses tree depth to control noise, which
is easily affected by tree fan-out. The decomposition method in References [30–32] considers the actual
distribution of the underlying spatial data, and divides data according to the actual position of the
spatial data points. However, these algorithms must be carried out under the protection of differential
privacy, otherwise it will reveal the privacy of the underlying data.
In conclusion, most of the spatial segmentation are affected by the actual data distribution.
The tree depth is usually used to control the Laplacian noise level, which leads to high computation
overhead and low availability. These methods do not consider well how to balance the noise error and
the uniform hypothesis error. Some decomposition methods, although taking into account the above
two kinds of error balance, did not consider how to use heuristic rules to adaptively set the equalization
parameters. When the count of spatial data reaches millions, these methods usually cannot obtain
accurate results. Although the above methods are able to give rigorous data availability theory bounds,
they did not perform well in data availability and efficiency on the actual data. In the vehicle-to-grid
network, electric vehicle location data is millions-level. The methods of spatial decomposition protect
the location privacy, usually leading to the availability of location data being especially low. In this
paper, we adopt the sampling algorithm based on differential privacy to achieve the balance between
large-scale spatial data and noise volume. To overcome the shortcomings of Laplacian noise controlled
by tree-depth in quadtree, we utilize sparse vector techniques to control when to partition the tree
node. Based on the vehicle-to-grid network structure in the smart grid, we propose a location privacy
protection model for electric vehicles in vehicle-to-grid networks adopting distributed differential
privacy technology.
3. Network Structure of V2G in Smart Grid
Vehicle-to-grid is a system that serves the energy interaction between electric vehicles and the
grid. Electric vehicles want to be able to get power when the grid load is at its nadir, and feed power
back to the grid when the grid load is at its peak [1]. At the same time, it hopes that the electric grid
will feed the electric energy back when the load is at its peak. When the electric vehicle and the grid
are in an energy interaction, they must establish real-time communication for the transmission of
relevant information, such as the status of the electric vehicle and the load of the electric network [10].
Therefore, the main activity in vehicle-to-grid is actually the two-way interaction related to energy and
information between EVs and the grid [8].
The vehicle-to-grid system is mainly concentrated in the distribution domain. In the vehicle-to-grid
network, a large number of electric vehicles, charging stations and parking lots jointly construct
a bidirectional power and communication network through a power distribution network and
a communication network, as shown in Figure 1.

energy and information between EVs and the grid [8].
The vehicle-to-grid system is mainly concentrated in the distribution domain. In the vehicle-togrid network, a large number of electric vehicles, charging stations and parking lots jointly construct
a bidirectional power and communication network through a power distribution network and a
communication network, as shown in Figure 1.

Energies 2018, 11, 2625

5 of 17

Information Flow

Current
Distribution
network

Control center

Aggregator 1

Charging station 1

Aggregator n

Parking lot

Charging station n

Figure 1. Network structure of V2G in smart grid.

(1) Control center: Control center is the most important component of the smart grid, solving
the dispatching and control problems of electric vehicles after they are connected to the grid. It is an
indispensable “brain” of the grid operation.
(2) Aggregators: On the one hand, aggregators can receive vehicle-to-grid service requests from
the smart grid control center to provide feedback-related information to the smart grid. On the
other hand, aggregators can gather vehicle-to-grid business services from the smart grid control
center after aggregating the information of multiple EVs, and then completing the subsequent related
resource scheduling.
(3) Distribution network: The distribution network is composed of overhead lines, cables, towers,
distribution transformers, isolation switch, reactive power compensators and some ancillary facilities.
It plays an important role in the distribution of power in the power grid and distributes the electric
energy to the electric vehicles in the vehicle to grid network.
(4) Charging station & charging parking lot: Charging stations and charging parking lots provide
electric vehicles with supplementary electric energy, in which there are many charging piles. The input
end is directly connected with the AC grid, and the output end is equipped with a charging plug for
charging electric vehicles.
(5) Electric vehicle: Electric vehicles are powered by on-board power and are equipped with
on-board battery packs. The batteries of a large number of EVs form a distributed, mobile power
warehouse that can be used to help the grid “fill the valley” (electric vehicles charge at night) during
down periods and “cut the peak” (electric cars discharge during the day) during peak periods.
The vehicle-to-grid system brings great economic benefits, social benefits and ecological benefits
to people, meanwhile, it also has the potential to leak users’ privacy. In order to meet the requirements
of power load adjustment (usually several million kilowatt hours), the vehicle to grid system must
ensure that a sufficient number of EVs are provided as energy storage resources within a given period
of time. Therefore, as shown in Figure 1, a certain number of EVs must be aggregated through an
aggregator, and monitor the related information of the EVs, such as the location of EVs, the state of
charge of the batteries, the expected departure time, and the real-time capacity of chargeable and
dischargeable, etc. so that the control center can optimally schedule the load requirements of the grid
on the basis of the EVs charge and discharge.
At the same time, the aggregators transfer the collected information to the control center. At this
point, if the original location data is uploaded, the control center can trace the user’s whereabouts and
analyze the user’s privacy information. In this paper, we mainly discuss the issue of privacy protection
of user location in vehicle-to-grid networks in this situation.

Energies 2018, 11, 2625

6 of 17

4. Location Privacy Protection Algorithm with Differential Privacy
According to the characteristics of EV location data in V2G network of smart grid and the shortage
of existing spatial decomposition algorithms, we propose a spatial data decomposition algorithm with
privacy protection in this chapter. Based on this, we propose a location privacy protection model of
EVs in the V2G network.
4.1. Data Preprocessing with Differential Privacy
Existing methods of spatial decomposition often deal with small-scale spatial data. However,
spatial data in V2G are usually large-scale and skewed. This often results in tree-based decomposition
methods that cannot be implemented or the availability of final query or analysis results are very low.
Therefore, how to decompose large-scale and skewed spatial data is a very big challenge. Therefore,
we take as many samples as possible with the sampling technique that satisfies the differential privacy
and spatially partition the samples for solving the problem.
4.1.1. Differential Privacy
Differential privacy means that one queries two different data sets with only one record different;
if query results are almost identical, the attacker cannot obtain the data of the individual by analyzing
the query results. This can achieve privacy protection. Assuming there are two datasets with only
one record different, the ratio of probabilities that query results on both datasets is close to 1, which
achieves differential privacy protection.
Definition 1. An algorithm A satisfies ε-differential privacy if, for any two neighboring datasets D and D’ and
for any possible output O of A, where Pr[•] denotes the probability of an event.


Pr( A( D ) = O)
ln
Pr[ A( D 0 ) = O]



≤ε

(1)

Definition 2. Let f be a function that maps a dataset D into a vector of real numbers. The global sensitivity of f
is defined as

S( f ) = maxk f ( D ) − f D 0 k1
(2)
D,D 0

where D and D’ are any two neighboring datasets, and k · k1 denotes the L1 norm.
Lemma 1. Let A1 , . . . , Ak be k algorithms, such that Ai satisfies εi -differential privacy (i∈[1, k]). Then, for the
k

same dataset, the sequential composition (A1 , . . . , Ak ) satisfies ( ∑ ε i )-differential privacy.
i =1

Lemma 2. Let A1 , . . . , Ak be k algorithms, such that Ai satisfies εi -differential privacy (i∈[1, k]). Then, for the
different datasets, the sequential composition (A1 , . . . , Ak ) satisfies (max ε i )-differential privacy.
Theorem 1. Let A satisfies ε-differential on dataset D. If take sample from D to get D’ with probability γ,
algorithm A satisfies ln(1 + γ(eε − 1))-differential on dataset D’.
Theorem 2. An algorithm A satisfies ε-differential privacy if,

A( D, di ) =





εu( D, di )

di : Pr[di ∈ Ω] ∝ exp
2∆u

(3)

where ∆u is the global sensitivity of u( D, di ), which is a scoring function, di is the output from the
output domain Ω.

Energies 2018, 11, 2625

7 of 17

4.1.2. Bernoulli Random Sampling Algorithm Based on Differential Privacy
For the problem of large-scale spatial data, our proposed decomposition method tries to
extract sufficient data as the decomposition data under the conditions of differential privacy.
The Bernoulli random sampling algorithm that satisfies differential privacy will be introduced in
detail as Algorithm 1.
Algorithm 1 Random Sampling Algorithm with Differential Privacy (D, ε)


ˆ = dˆ1 , dˆ2 , . . . , dˆm after implementing multiple Bernoulli experiments with
1
Obtain spatial data sample D
probability γ;
2
Calculate ε γ = ln(γ + eε − 1) − ln γ on the basis of Theorem 1.

Firstly, we determine the sampling probability γ, and then make the Bernoulli experiment with γ
on D. If the experiment is successful, obtain the spatial sample, otherwise, abandon the sample. Finally,
calculate the privacy cost ε γ required for the entire space decomposition. The key of the process is
ε
how to make the sampling process to meet the differential
privacy. Since ε
γ = ln(γ + e − 1) − lnγ,



we bring ε γ into ln(1 + γ(eε − 1)), and obtain ln 1 + γ eln (γ+e
the proposed sampling process satisfies ε-differential privacy.

ε −1)−ln γ

−1

= ε. So we can prove

4.2. Spatial Decomposition Algorithm BQ-Tree
By studying the existing spatial decomposition algorithms, we know that the existing algorithms
do not work well in dealing with millions of spatial data. In this part, we combine the proposed random
sampling algorithm with the quadtree algorithm, and propose a new spatial decomposition algorithm
BQ-tree. It can overcome the problem that the traditional quadtree algorithm cannot deal with a huge
number of spatial data. We also prove that the BQ-tree algorithm satisfies the differential privacy.
4.2.1. The Quadtree Algorithm
The specific algorithm of quadtree is as Algorithm 2. It has four input parameters, which are:
(1) a dataset D of spatial data distributed in a multidimensional domain Ω, (2) the Laplacian noise
of size ε added to the tree, (3) the threshold θ of splitting node in the tree, (4) the threshold h of the
maximum height of the tree. The algorithm returns a quadtree, each node contains two parts of
information, namely the sub-domain corresponding to v, and the value of the number of spatial data
in the sub-domain which is added noise. At the same time, the depth of v is defined as the maximum
distance between v and the root node. It is recorded as depth (v).
4.2.2. The BQ-Tree Algorithm
Compared with the traditional quadtree algorithm, the proposed algorithm first initializes the
quadtree based on the sampled dataset, and calculates the size of added noise. BQ-tree specific
establishment process is as Algorithm 2:
Algorithm 2 BQ-Tree (D, ε, θ, h)
1
2
3
4
5
6
7
8
9
10

ˆ on basis of Algorithm 1;
Compute ε γ and D
ˆ and mark v1 as unvisited;
initialize a quadtree T with a root node v1 on dataset D,
while there exists an unvisited node v do
mark v as visited;
compute the number c(v) of data points that are contained in dom(v);
compute a noisy version of c(v): cˆ(v) = c(v) + Lap(ε);
if cˆ(v) > θ and depth(v) < h − 1 then
split v, and add its children to T;
mark the children of v as unvisited;
return T

Energies 2018, 11, 2625

8 of 17

ˆ by using Algorithm
The algorithm starts by computing the privacy cost ε γ and sample dataset D
ˆ and the root node is set to unvisited.
1 proposed in Section 4.1.2. Next, the quadtree is initialized on D
The subsequent part of the algorithm consists of a number of iterations. In each iteration, we examine
if there are unvisited nodes in the tree. If such v exists, we mark the nodes as visited state, calculate
the number of space points, and add ε γ noise to the number. After that, we split v if the following
two conditions simultaneously hold. One of the conditions is that the number cˆ(v) is greater than the
threshold of decomposition θ and the other is the height of the tree is less than the height threshold h
of the tree. If both of the above conditions are met, then we generate v’s children and insert them into
T as unvisited nodes. Finally, when all node have been visited, we return the quadtree.
According to Section 4.1.2, we know that the sampling process satisfies the differential privacy.
To prove that the overall BQ-tree algorithm satisfies the differential privacy, we only need to prove that
step 6 in Algorithm 2 satisfies the differential privacy. Step 6 adds a noise of Lap(ε γ ) size to each node
because the count up to h nodes is affected when adding or removing a data point in D. Combining
the differential privacy Lemma 1 and Lemma 2, Step 6 satisfies ε γ -differential privacy. Then, according
to Theorem 1, the proposed algorithm satisfies ε-difference privacy.
4.3. Spatial Decomposition Algorithm BQ-Tss
The existing tree-based spatial decomposition methods usually adopt tree depth to control
Laplacian noise. However, it is very difficult to set a proper tree depth. If artificially directly adjust the
depth of the tree, the adjustment process will violate the differential privacy and thus the sensitive
information in the spatial data cannot be protected. If we can add noise for the nodes in the tree
without depending on the depth of the tree to control the noise, this will control the added noise better.
In this section, we use sparse vector techniques to set the decomposition conditions of the nodes in the
tree to solve the problem of tree-depth dependent noise control.
4.3.1. Sparse Vector Technology
Sparse vector technique is commonly used to respond to a limited number of count queries
greater than a certain threshold. The technique consists of two main steps: One is to find a suitable
threshold θ and obtain θe after adding noise; the other one is to obtain ce(v) after adding noise to each
query result c(v ) and
compare it with the noise threshold. One of comparison results is to output ce(v)
2
ˆ otherwise an identifier ⊥ is output. The specific application of sparse vector
if = c(v) + Lap
≥ θ,
ε1

technology in our work is shown as Equation (4):
(
cˆ(v) =

c(v) + Lap

⊥others


2
ε1

i f c(v) + Lap


2
ε1

≥ θˆ

(4)

4.3.2. The BQ-Tss Algorithm
In order to overcome the shortcomings of the original algorithm, which control noise dependent
on the depth of tree, we combine the sparse vector technique with the algorithm shown in Section 4.2.2,
and propose a new spatial decomposition algorithm BQ-Tss. The specific algorithm is shown as
Algorithm 3.

Energies 2018, 11, 2625

9 of 17

Algorithm 3 BQ-Tss (D, ε, θ)
1
2
3
4
5
6
7
8
9
10
11

ˆ on basis of Algorithm 1;
Compute ε γ and D
ˆ and mark v1 as unvisited;
initialize a quadtree T with a root node v1 on dataset D,
while there exists an unvisited node v do
mark v as visited;
compute the number c(v) of data points
are contained in dom(v);
that
2
ˆ
compute noise threshold θ = θ + Lap ε γ ;

compute a noisy version of c(v): cˆ(v) = c(v) + Lap ε2γ ;
if cˆ(v) > θˆ and v is not the leaf then
split v, and add its children to T;
mark the children of v as unvisited;
return T

In the vehicle-to-grid network, there exists large-scale skewed data, which most existing spatial
decomposition algorithms cannot handle. In BQ-Tss, we use the privacy-based random sampling
algorithm, which is proposed in Section 4.1, to solve this problem. We use random sampling to obtain
enough electric vehicles’ position data from raw data, which represents the overall data distribution.
The selected data can be used to replace raw data. Then, we perform spatial decomposition on the
selected data.
Tree-based spatial decomposition algorithms usually control the Laplace noise by the depth of
the tree, which is very difficult to determine. In BQ-Tss, we use a different way to control the size of
noise. The method is based on sparse vector technology. When adding noise to the nodes of tree, it can
provide the appropriate size of noise without depending on the depth of the tree. Therefore, compared
with other spatial segmentation algorithms, BQ-Tss can handle large-scale skew data in V2G, and it can
ensure the addition of appropriate scale noise, while realizing the protection of location data privacy.
According to Algorithm 3, the BQ-Tree satisfies the differential privacy. The newly proposed
algorithm uses extra privacy cost only on the SVT step. Therefore, BQ-Tss can be inferred to satisfy
ε-differential privacy as long as it is proved that SVT satisfies ε γ -differential privacy.
In BQ-Tss algorithm, we use SVT technology to determine whether the tree node should be
divided, and this seems likely to judge yes or no. Therefore, to prove conveniently, we use the binary
ˆ then xi = 1, that
vector V = h x1 , x2 , . . . , xt i to record whether the nodes should be divided. If cˆ(v) > θ,
represents node vi is divided; otherwise xi = 0, which represents node vi is not divided and vi is a leaf
node. Given the two adjacent spatial datasets D and D’, Pr1 (v) and Pr2 (v) denote the probabilities of
SVT acting on D and D’ with the output of V, respectively. Let x <i denote the first (i − 1) responses in
vector V. We can conclude the distribution of cˆ(vi ) and θˆ satisfies Laplace distribution based on the
Equation (5) shown as follows:

Pr1 (v)
=
Pr2 (v)

t


∏ Pr1 xi = 1or0 x <i





Pr1 xi = 1 x <i
Pr1 xi = 0 x <i


×∏

=∏


Pr2 xi = 1 x <i
Pr2 xi = 0 x <i
<
i

Pr
x
=
1or0
x
∏ 2 i

i =1
t

(5)

i =1

We suppose that x is a decomposition threshold on D, let Hi (x) denote the probability of xi = 1 on
D, and Hi0 ( x ) denote the probability of xi = 1 on D 0 . Therefore, Hi ( x ) can be described as the following
Equation (6), Lap(λ) represents the independent noise generated by the Laplace distribution.












Hi ( x ) = Pr xi = 1 x <i = Pr cˆ(vi ) ≥ x x <i = Pr Lap(λ) + c(vi ) ≥ x x <i

(6)

Energies 2018, 11, 2625

10 of 17

Based on the Laplace distribution, λ = ε2 and f (y : u, λ) =
1
represented as Equation (7):

Z ∞
2
dy
Hi ( x ) =
f y : c ( v i ),
ε1
x

1




|y−u|
exp − λ , Hi (x) can be
(7)

According to the global sensitivity Definition 2, the sensitivity of the count c(v) is 1, that is
∆ = 1. Let c(v) and c0 (v) denote the counts of nodes vi on D and D 0 respectively, and c0 (v) = c(v) + 1.
Therefore, µ = λ + 1. Hi ( x ) can be expressed as the following Equation (8):
Hi ( x ) =

Z ∞
x +1



Z ∞
2
2
0
f u : c(vi ) + 1,
dµ =
f u : c (vi ) + 1,
dµ = H 0 i ( x + 1)
ε1
ε1
x +1


(8)



And ∏ Pr1 xi = 1 x <i can be expressed as the following Equation (9):


x = 1 x <i
∏ Pr
R ∞1 i
= −∞ Pr ( x )∏ Hi ( x )dx
R∞
= −∞ Pr ( x )∏ Hi0 ( x + 1)dx
R ∞
≤ exp ε21 −∞ Pr ( x + 1)∏ H 0 i ( x + 1)dx
R ∞
= exp ε21 −∞ Pr ( x )∏ H 0 i ( x )dx



= exp ε21 ∏ Pr2 xi = 1 x <i

(9)

Similarly, we can obtain Equation (10) as follows:

∏ Pr1






ε




xi = 0 x <i ≤ exp 1 ∏ Pr2 xi = 0 x <i
2

(10)

And the Equation (11) as follows:
Pr1 (V )
≤ exp(ε 1 )
Pr2 (V )

(11)

So, we can obtain Equation (12) as follows:
Pr1 (V ) ≤ exp(ε 1 ) × Pr2 (V )

(12)

As we can see from the Definition 1 of differential privacy and Equation (12), SVT operation
satisfies ε γ -differential privacy. Therefore, BQ-Tss satisfies ε-difference privacy.
4.4. Location Protection Model in V2G Network
In the V2G network, a new network equipment is added between the electric vehicle and the smart
grid control system, commonly referred to as an aggregator. V2G manager through the aggregator to
monitor the location of the EV, charging status and other related information so that the manager can
optimally schedule EVs’ charge and discharge according to the load requirements of the grid. Each
aggregator’s connected charging equipment and electric vehicles can compose a small independent
network. Therefore, if we can ensure the privacy of electric vehicles in each independent network is
secure, the location privacy of electric vehicles in the whole V2G network can be guaranteed. In this
section, we apply the distributed differential privacy technology to the location privacy protection
algorithm proposed in Section 4.3. Combining with the specific V2G network structure, we propose
a EVs location privacy protection model with differential privacy in the V2G network.

Energies 2018, 11, x FOR PEER REVIEW

11 of 18

4.4.1. Distributed Differential Privacy

 1.25 
Theorem 3. Let    0,1 be arbitrary. For c 2  2ln 
 , the Gaussian Mechanism with parameter
11 of 17
  
c f
  2 is  ,   -differentially private.

4.4.1. Distributed
Differential Privacy

Energies 2018, 11, 2625


are honest, if each party generates gaussian
Assuming that all parties in a distributed structure
c∆2 f
Theorem 3. Let ε ∈ (0, 1) be arbitrary. For c2 > 2 ln 1.25
δ  , the gaussian mechanism with parameter δ ≥ ε
distribution noise with a standard deviation of  i 
and t represents the number of participants
is (ε, δ)-differentially private.
t
who generate the noise, then the overall standard deviation of noise is σ, that is to say, the distributed
Assuming that all parties in a distributed structure are honest, if each party generates gaussian
structure satisfies the differential privacy of  ,   as a whole.
distribution noise with a standard deviation of δi = √δ and t represents the number of participants
t
who generate the noise, then the overall standard deviation of noise is σ, that is to say, the distributed
4.4.2. EVs’ Location Privacy Protection Algorithm with Differential Privacy
structure satisfies the differential privacy of (ε, δ) as a whole.
In the V2G network architecture proposed above, we assume that each aggregator is
4.4.2. EVs’ Location Privacy Protection Algorithm withDifferential Privacy
trustworthy. If we assign a privacy budget of  i 
to each aggregator and t represents the
t assume that each aggregator is trustworthy.
In the V2G network architecture proposed above, we
number
of aaggregators,
theof overall
V2G
location
protectionthealgorithm
the
If
we assign
privacy budget
δi = √δ to
eachnetwork
aggregator
and t represents
number ofsatisfies
aggregators,
t
differential
privacy
of  location
,  .
the
overall V2G
network
protection algorithm satisfies the differential privacy of (ε, δ).
We assign
assign the
the appropriate
appropriate privacy
privacy budget to each aggregator
aggregator network based on distributed
differential privacy. Combining
Combining the
the BQ-Tss
BQ-Tss algorithm
algorithm proposed
proposed in Section 4.3, we propose EVs
location
with
differential
privacy
in V2Ginnetwork.
The specific
location protection
protectionalgorithm
algorithm
with
differential
privacy
V2G network.
Thelocation
specificprotection
location
algorithm
shown inisFigure
protection is
algorithm
shown2.in Figure 2.
Start
Compute the privacy budget 11
assigned to each aggregator
Compute privacy budget 11
and sample data
Initialize a
Quadtree T

If there exists an
unvisited node v
Yes

Compute noise threshold
No
No

Compute a noisy version of c(v):

If
and
v is not the leaf

Split v, and add its
children to T
Return T
End

Figure
Privacy.
Figure 2. EVs
EVs Location
Location Privacy
Privacy Protection
Protection Algorithm with Differential Privacy.

5. Experimental Results and Analysis
Our experiments were conducted on an 8-core Intel i7-3612 CPU (2.10 GHz), 8G RAM, Win7
system platform and all algorithms were implemented in Python. The experiment used collected 1500

week, with a total of 600,000 messages.
The relative error (RE) is used to measure the data availability of quardtree, BQ-tree, DP-tree
and BQ-Tss algorithms. The relative error is calculated using Equation (13):





RE Q  D  

Energies 2018, 11, 2625

Q  D  Q  D

12 of 17
(13)

max Q  D  , 

where
denotes
the trueand
range
result
on
and
denotesvehicles
the noise
of the
Q  D  posts
public
charging
in Beijing
thequery
charging
position
of
100,000 electric
in result
a certain
week,
with
a total
of on
600,000
range
query
is a smoothing factor whose value is 0.1% of the experimental dataset size.
D . messages.
In relative
this experiment,
Bernoulli
random
sampling
probability
as 1% and
privacy
budgetand
The
error (RE)we
is set
used
to measure
the data
availability
of quardtree,
BQ-tree,
DP-tree
 values
 is(13):
parameters
0.1, 0.3,
0.5,is0.7,
1.0 and using
1.2. When
0.5, we extract 16,000 position
BQ-Tss
algorithms.
The of
relative
error
calculated
Equation
information from the data set. The overall position maps of the electric
vehicle, before and after noise



e
addition, are shown in Figure 3a,b, respectively.
The
local
position
maps
are shown in Figure 4a,b,


Q( D ) − Q( D )
e(D) =
RE Q
(13)
respectively.
max{ Q( D ), ∆}
We can see from Figure 3a,b that, after adding noise, the change of the overall position
distribution is slight. It indicates that the position data aftere noise addition is relatively accurate. If
where Q( D ) denotes the true range query result on D and Q( D ) denotes the noise result of the range
we use position data in Figure 3b instead of that in Figure 3a, the query of data can still achieve high
query on D. ∆ is a smoothing factor whose value is 0.1% of the experimental dataset size.
accuracy. To better illustrate this point, we have partially enlarged the overall image to generate
In this experiment, we set Bernoulli random sampling probability as 1% and privacy budget
Figure 4a,b. In Figure 4a,b, we can clearly see that each position coordinate has a slight change after
parameters ε values of 0.1, 0.3, 0.5, 0.7, 1.0 and 1.2. When ε is 0.5, we extract 16,000 position information
adding noise. Applying the spatial decomposition algorithm, we divide the small area into four parts.
from
the data
overall
positionvehicles
maps ofinthe
electric
before and
aftertonoise
addition,
In each
part,set.
theThe
number
of electric
Figure
4b vehicle,
is approximately
equal
the number
inare
shown
in
Figure
3a,b,
respectively.
The
local
position
maps
are
shown
in
Figure
4a,b,
respectively.
Figure 4a. Therefore, when querying the position data in Figure 3b, the accuracy remains very high.

(a)

(b)

EnergiesFigure
2018,
11,
xThe
FOR
PEER REVIEW
Figure
Theoverall
overall
position maps of EVs.
(b)(b)
after
noise
addition.
3.3.
position
EVs. (a)
(a)before
beforenoise
noiseaddition;
addition;
after
noise
addition.

(a)

13 of 18

(b)

Figure
4. The
local
position
maps
of EVs.
before
noise
addition;
after
noise
addition.
Figure
4. The
local
position
maps
of EVs.
(a)(a)
before
noise
addition;
(b)(b)
after
noise
addition.

WeWe
canset
seethe
from
Figure
3a,b that,
after
adding
noise,
the
change
of the
overall
range
of query
cover
1%, 3%,
5%,
7%,
10% and
12%
of theposition
data setdistribution
respectively,
Q to
is slight.
It
indicates
that
the
position
data
after
noise
addition
is
relatively
accurate.
If
we
use
position
and 5000 queries are randomly generated within each query range.
data in We
Figure
3b instead
of that inalgorithm
Figure 3a,with
the query
of data
can stilland
achieve
highalgorithms.
accuracy. To
betterthe
compare
our BQ-Tss
quardtree,
BQ-tree,
DP-tree
When
illustrate
this
point,
we
have
partially
enlarged
the
overall
image
to
generate
Figure
4a,b.
In
Figure
4a,b,the
fixed-range query is fixed, we obtain the relative error of four different algorithms by changing
weprivacy
can clearly
see
that
each
position
coordinate
has
a
slight
change
after
adding
noise.
Applying
the
budget  value, and then compare the data availability of the each algorithm.
spatial The
decomposition
algorithm,
wequery
divide
the small
area
parts.
In eachAs
part,
figure above
shows the
range
results
of into
EVs four
location
dataset.
canthe
be number
seen from

Figures 5–7, when the query range is fixed to 1%, 5%, 10%,  changes from 0.1 to 1.2, the accuracy
of the proposed algorithm is almost three times that of the BQ-tree algorithm, and is nearly 10 times
more than the DP-tree and quardtree algorithms. Especially when the query range is 1%, it is nearly
13 times more than the quardtree and DP-tree algorithm. From this we can conclude that as the range
of query increases, the query accuracy of the algorithm is improved. When the query range is fixed,

Energies 2018, 11, 2625

13 of 17

(a)

(b)

4. The
position
maps of EVs. (a) equal
before to
noise
noise
of electricFigure
vehicles
in local
Figure
4b is approximately
theaddition;
number(b)
in after
Figure
4a.addition.
Therefore, when
querying the position data in Figure 3b, the accuracy remains very high.
We set the range of query Q to cover 1%, 3%, 5%, 7%, 10% and 12% of the data set respectively,
We set the range of query Q to cover 1%, 3%, 5%, 7%, 10% and 12% of the data set respectively,
and
within each
each query
query range.
range.
and 5000
5000 queries
queries are
are randomly
randomly generated
generated within
We
compare
our
BQ-Tss
algorithm
with
quardtree,
BQ-tree,
and DP-tree
DP-tree algorithms.
algorithms. When
We compare our BQ-Tss algorithm with quardtree, BQ-tree, and
When the
the
fixed-range
query
is
fixed,
we
obtain
the
relative
error
of
four
different
algorithms
by
changing
the
fixed-range query is fixed, we obtain the relative error of four different algorithms by changing the
privacy
value,
and
then
compare
data
availability
each
algorithm.
privacy budget
budget εvalue,
and
then
compare
thethe
data
availability
of of
thethe
each
algorithm.
The
EVs location
location dataset.
dataset. As
The figure
figure above
above shows
shows the
the query
query range
range results
results of
of EVs
As can
can be
be seen
seen from
from

Figures
5–7,
when
the
query
range
is
fixed
to
1%,
5%,
10%,
changes
from
0.1
to
1.2,
the
accuracy
Figures 5–7, when the query range is fixed to 1%, 5%, 10%, ε changes from 0.1 to 1.2, the accuracy
of
of
proposed
algorithm
almostthree
threetimes
timesthat
thatofofthe
theBQ-tree
BQ-treealgorithm,
algorithm, and
and is
is nearly
nearly 10
10 times
thethe
proposed
algorithm
is is
almost
times
more
more than
than the
the DP-tree
DP-tree and
and quardtree
quardtree algorithms.
algorithms. Especially
Especially when
when the
the query
query range
range is
is 1%,
1%, itit is
is nearly
nearly
13
times
more
than
the
quardtree
and
DP-tree
algorithm.
From
this
we
can
conclude
that
as
the
13 times more than the quardtree and DP-tree algorithm. From this we can conclude that as the range
range
of
of query
query increases,
increases, the
the query
query accuracy
accuracy of
of the
the algorithm
algorithm is
is improved.
improved. When
When the
the query
query range
range is
is fixed,
fixed,
the
query
accuracy
of
the
algorithm
decreases
with
the
increasing
of
the
privacy
budget.
Under
the query accuracy of the algorithm decreases with the increasing of the privacy budget. Under the
the
same
same condition,
condition, the
the accuracy
accuracy of
of our
our proposed
proposed algorithm
algorithm is
is obviously
obviously better
better than
than that
that of
of quardtree
quardtree
and
and DP-tree,
DP-tree, and
and is
is also
also superior
superior to
to BQ-tree.
BQ-tree. When
When the
the query
query range
range is
is fixed
fixed at
at 10%,
10%, the
the algorithm
algorithm can
can
achieve
an
accuracy
of
99.97%,
which
shows
that
the
proposed
algorithm
is
suitable
for
achieve an accuracy of 99.97%, which shows that the proposed algorithm is suitable for aa big
big data
data
environment
environment and
and can
can guarantee
guarantee the
the data
data availability
availability under
under the
the condition
condition of
of protecting
protecting the
the privacy
privacy of
of
the
location
data.
the location data.
0.04

Our proposed
BQ-Tree
QuardTree
DP-Tree

relative error

0.03

0.02

0.01

0
0.1

0.3

Energies 2018, 11, x FOR PEER REVIEW

0.08

0.5

0.7

1

1.2

14 of 18

privacy budget

Figure 5. Query range Q = 1%.
Figure 5. Query range Q = 1%.
Our proposed
BQ-Tree
QuardTree
DP-Tree

0.07

relative error

0.06

0.05

0.04

0.03

0.02

0.01

0
0.1

0.3

0.5

0.7

1

privacy budget

Figure 6. Query range Q = 5%.
Figure 6. Query range Q = 5%.

0.12

0.1

Our proposed
BQ-Tree
QuardTree

1.2

0
0.1

0.3

0.5

0.7

1

1.2

privacy budget

Energies 2018, 11, 2625

14 of 17

Figure 6. Query range Q = 5%.

0.12

Our proposed
BQ-Tree
QuardTree
DP-Tree

0.1

relative error

0.08

0.06

0.04

0.02

0
0.1

0.3

0.5

0.7

1

1.2

privacy budget

Figure 7. Query range Q = 10%.

Figure 7. Query range Q = 10%.

Figures 8–10 shows that when the query range is changed from 1% to 12% and the ε is fixed to 0.1,
0.5, and
1.0 respectively,
ofrange
BQ-Tss
nearly twice
of12%
BQ-tree,
which
nearly
Figures
8–10 shows the
thatquery
whenaccuracy
the query
is is
changed
from that
1% to
and the
 isisfixed
to
0.1,times
0.5, and
respectively,
the query
accuracy
of BQ-Tss
is nearly
twiceinthat
of BQ-tree,
is
12
that 1.0
of the
quardtree and
DP-tree
algorithm.
In addition,
as shown
Figures
6–8, thewhich
BQ-tree
nearly
12 times
that
of the quardtree
andand
DP-tree
algorithm.
In addition,
shown in
Figures
BQalgorithm
is also
superior
to quardtree
DP-tree.
From this,
we can as
conclude
that
when6–8,
the the
privacy
tree
algorithm
alsoaccuracy
superioroftothe
quardtree
and
DP-tree.as
From
this, we
can increases.
conclude that
the
budget
is fixed,isthe
algorithm
decreases
the query
scope
Thewhen
accuracy
privacy
budget is
fixed, the
the algorithm
decreases
as the
query
scope
increases.
The
of the proposed
algorithm
is accuracy
obviouslyofsuperior
to quardtree,
DP-tree
and
BQ-tree
when
the privacy
accuracy
the proposed
is obviously
quardtree,
and
BQ-tree
when
budget is of
same.
When the algorithm
privacy budget
is fixed superior
at 1.0, thetoaccuracy
rateDP-tree
of 99.93%
can
be achieved,
the privacy
same. When
the privacy
is fixed
at 1.0,problem
the accuracy
rate
of 99.93%well.
can
which
showsbudget
that theissampling
technique
we usebudget
can avoid
the skew
of data
distribution
be achieved,
showsdecompose
that the sampling
technique
weSVT
use technology,
can avoid the
skew
data
We
also avoidwhich
multi-level
privacy cost
by using
which
is problem
obviouslyofbetter
Energies
2018, similar
11,
x FOR
PEER
REVIEW
15
of 18
distribution
well.
We
also
avoidThis
multi-level
cost by
using SVT technology,
which
than other
algorithms.
can alsodecompose
prove, evenprivacy
in the case
of unbalanced
data distribution,
is
obviously
better
than
similar
This can also prove, even in the case of unbalanced
that
our method
can
stillother
achieve
highalgorithms.
query accuracy.
data distribution, that our method can still achieve high query accuracy.
0.14

0.12

Our proposed
BQ-Tree
QuardTree
DP-Tree

relative error

0.1

0.08

0.06

0.04

0.02

0
1%

3%

5%

7%

quary shapes

Figure 8. Privacy budget ε = 0.1.
Figure 8. Privacy budget  = 0.1.

0.05

relative error

0.04

0.03

0.02

Our proposed
BQ-Tree
QuardTree
DP-Tree

10%

12%

0
1%

Energies 2018, 11, 2625

0.05

relative error
relative error

0.05
0.04

0.04
0.03

3%

5%

7%

quary budget
shapes  = 0.1.
Figure 8. Privacy

10%

12%

Figure 8. Privacy budget  = 0.1.

15 of 17

Our proposed
BQ-Tree
QuardTree
DP-Tree
Our proposed
BQ-Tree
QuardTree
DP-Tree

0.03
0.02

0.02
0.01

0.010
1%

3%

5%

7%

10%

12%

10%

12%

10%

12%

Figure
10. Privacy
budget
ε = 1.0. 10%
3%
5%
7%

12%

quary shapes
0
1%

0.04

0.035

relative error
relative error

0.04
0.03
0.035
0.025

5%

7%

Figure 9. Privacy budget ε = 0.5.
Figure 9. Privacy budget  = 0.5.
Our proposed
BQ-Tree
QuardTree
DP-Tree
Our proposed
BQ-Tree
QuardTree
DP-Tree

0.03
0.02
0.025
0.015
0.02
0.01
0.015
0.005
0.01
0
1%
0.005

0
1%

6. Conclusions

3%

quary budget
shapes  = 0.5.
Figure 9. Privacy

3%

5%

7%

quary shapes

quary shapes

The privacy-protected spatial decomposition algorithm for V2G networks needs to be able
to handle large-scale skewed data in V2G, and add the appropriate noise to nodes in the tree
without relying on the depth of the tree. In order to meet these requirements, we propose a spatial
decomposition algorithm called BQ-Tss. Compared with other existing spatial decomposition
algorithms, BQ-Tss algorithm achieves higher query accuracy. When adding the same noise, the error
rate of BQ-tree is twice that of BQ-Tss, and quardTree and DP-tree are 10 times that of BQ-Tss. Therefore,
our proposed algorithm can deal with large-scale skewed data better and get a higher precision query
result. Under the slight noise of different scales, the accuracy of our query can be kept at around 99.9%.
The proposed algorithm is based on the quad-tree spatial segmentation algorithm, including a random
sampling algorithm with privacy protection and a method for segmenting nodes in a tree based on
a sparse vector technique. Our proposed algorithm can overcome the shortcomings of the existing
spatial segmentation algorithm and is more suitable for V2G networks. Therefore, our proposed
algorithm can guarantee the normal control of the V2G network by the grid control center, while
ensuring the privacy of the location data.
Author Contributions: Conceptualization, Y.L.; Methodology, Y.L., Y.W. and P.Z; Validation, Y.W. and P.Z.; Formal
Analysis, Y.W. and P.Z.; Investigation, Y.W. and P.Z; Resources, P.Z.; Data Curation, Y.W.; Writing-Original
Draft Preparation, Y.M.; Writing-Review & Editing, Y.L.; Visualization, Y.W.; Supervision, P.Z.; Project
Administration, Y.L.

Energies 2018, 11, 2625

16 of 17

Funding: This research was supported by the Fundamental Research Funds for the Central Universities
(2018ZD06).
Acknowledgments: This work was supported by the Fundamental Research Funds for the Central Universities
(2018ZD06).
Conflicts of Interest: The authors declare no conflict of interest.

References
1.
2.
3.
4.
5.
6.

7.
8.
9.
10.
11.
12.

13.

14.
15.

16.

17.

18.

Harighi, T.; Bayindir, R.; Padmanaban, S.; Mihet-Popa, L.; Hossain, E. An overview of energy scenarios,
storage systems and the infrastructure for vehicle-to-grid technology. Energies 2018, 11, 2174. [CrossRef]
Rottondi, C.; Fontana, S.; Verticale, G. Enabling privacy in vehicle-to-grid interactions for battery recharging.
Energies 2014, 7, 2780–2798. [CrossRef]
Geske, J.; Schumann, D. Willing to participate in vehicle-to-grid (V2G)? Why not! Energy Policy 2018, 120,
392–401. [CrossRef]
Child, M.; Nordling, A.; Breyer, C. The impacts of high V2G participation in a 100% renewable Åland energy
system. Energies 2018, 11, 2206. [CrossRef]
Nefedov, E.; Sierla, S.; Vyatkin, V. Internet of energy approach for sustainable use of electric vehicles as
energy storage of prosumer buildings. Energies 2018, 11, 2165. [CrossRef]
Paterakis, N.G.; Pappi, I.N.; Erdinç, O.; Godina, R.; Rodrigues, E.M.G.; Catalão, J.P.S. Consideration of the
impacts of a smart neighborhood load on transformer aging. IEEE Trans. Smart Grid 2016, 7, 2793–2802.
[CrossRef]
Blasius, E. Possible role of power-to-vehicle and vehicle-to-grid as storages and flexible loads in the German
110 kV distribution grid. Front. Energy 2017, 11, 146–154. [CrossRef]
Aziz, M.; Oda, T.; Mitani, T.; Watanabe, Y.; Kashiwagi, T. Utilization of electric vehicles and their used
batteries for peak-load shifting. Energies 2015, 8, 3720–3738. [CrossRef]
Zhang, Y.; Li, J.; Zheng, D.; Li, P.; Tian, Y. Privacy-preserving communication and power injection over
vehicle networks and 5G smart grid slice. J. Netw. Comput. Appl. 2018, 122, 50–60. [CrossRef]
Roman, L.F.A.; Gondim, P.R.L.; Lloret, J. Pairing-based authentication protocol for V2G networks in smart
grid. Ad Hoc Netw. 2018. [CrossRef]
Yang, Z.Y.; Yu, S.C.; Lou, W.J.; Liu, C. P2 : Privacy-Preserving communication and precise reward architecture
for V2G networks in smart grid. IEEE Trans. Smart Grid 2011, 2, 697–706. [CrossRef]
Tseng, H.R. A secure and privacy-preserving communication protocol for V2G networks. In Proceedings
of the 2012 IEEE Wireless Communications and Networking Conference (WCNC), Shanghai, China,
1–4 April 2012.
Nicanfar, H.; Hosseininezhad, S.; Talebifard, P.; Leung, V.C.M. Robust privacy-preserving authentication
scheme for communication between electric vehicle as power energy storage and power stations.
In Proceedings of the 2013 IEEE Conference on Computer Communications Workshops (INFOCOM
WKSHPS), Turin, Italy, 14–19 April 2013.
Au, M.H.; Liu, J.K.; Fang, J.; Jiang, Z.L.; Susilo, W.; Zhou, J. A new payment system for enhancing location
privacy of electric vehicles. IEEE Trans. Veh. Technol. 2014, 63, 3–18. [CrossRef]
Stegelmann, M.; Kesdogan, D. Location privacy for vehicle-to-grid interaction through battery management.
In Proceedings of the 2012 Ninth International Conference on Information Technology—New Generations,
Las Vegas, NV, USA, 16–18 April 2012.
Stegelmann, M.; Kesdogan, D. V2GPriv: Vehicle-to-Grid privacy in the smart grid. In Proceedings of the 4th
International Symposium, CSS 2012, Melbourne, Australia, 12–13 December 2012; Cyberspace Safety and
Security, Xiang, Y., Lopez, J., Kuo, C.-C.J., Zhou, W., Eds.; Springer: Berlin/Heidelberg, Germany, 2012.
Xiao, Y.; Xiong, L.; Yuan, C. Differentially private data release through multidimensional partitioning.
In Proceedings of the 7th VLDB Workshop, Workshop on Secure Data Management, Singapore,
17 September 2010; Secure Data Management, Jonker, W., Petkovi´c, M., Eds.; Springer: Berlin/Heidelberg,
Germany, 2010.
Qardaji, W.; Yang, W.; Li, N. Differentially private grids for geospatial data. In Proceedings of the 2013 IEEE
29th International Conference on Data Engineering (ICDE), Brisbane, Australia, 8–12 April 2013.

Energies 2018, 11, 2625

19.

20.
21.

22.
23.

24.

25.

26.
27.
28.
29.

30.
31.
32.

17 of 17

Mir, D.J.; Isaacman, S.; Cáceres, R.; Martonosi, M.; Wright, R.N. DP-WHERE: Differentially private modeling
of human mobility. In Proceedings of the 2013 IEEE International Conference on Big Data, Silicon Valley, CA,
USA, 6–9 October 2013.
To, H.; Ghinita, G.; Shahabi, C. A framework for protecting worker location privacy in spatial crowdsourcing.
Proc. VLDB Endow. 2014, 7, 919–930. [CrossRef]
Cormode, G.; Procopiuc, C.; Srivastava, D.; Shen, E.; Yu, T. Differentially private spatial decompositions.
In Proceedings of the 2012 IEEE 28th International Conference on Data Engineering, Washington, DC, USA,
1–5 April 2012.
Fan, L.; Bonomi, L.; Xiong, L.; Sunderam, V. Monitoring web browsing behavior with differential privacy.
In Proceedings of the 23rd International Conference on World Wide Web, Seoul, Korea, 7–11 April 2014.
Zhang, J.; Xiao, X.; Xie, X. PrivTree: A differentially private algorithm for hierarchical decompositions.
In Proceedings of the 2016 International Conference on Management of Data, San Francisco, CA, USA,
26 June–1 July 2016.
Lee, J.; Clifton, C.W. Top-k frequent itemsets via differentially private FP-trees. In Proceedings of the 20th
ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA,
24–27 August 2014.
Chen, R.; Xiao, Q.; Zhang, Y.; Xu, J. Differentially private high-dimensional data publication via
sampling-based inference. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge
Discovery and Data Mining, Sydney, Australia, 10–13 August 2015.
Hay, M.; Rastogi, V.; Miklau, G.; Dan, S. Boosting the accuracy of differentially private histograms through
consistency. Proc. Vldb Endow. 2010, 3, 1021–1032. [CrossRef]
Qardaji, W.; Yang, W.; Li, N. Understanding hierarchical methods for differentially private histograms.
Proc. VLDB Endow. 2013, 6, 1954–1965. [CrossRef]
Kellaris, G.; Papadopoulos, S. Practical differential privacy via grouping and smoothing. Proc. VLDB Endow.
2013, 6, 301–312. [CrossRef]
Peng, S.; Yang, Y.; Zhang, Z.; Winslett, M.; Yu, Y. DP-tree: Indexing multi-dimensional data under differential
privacy (abstract only). In Proceedings of the 2012 ACM SIGMOD International Conference on Management
of Data, Scottsdale, AZ, USA, 20–24 May 2012.
To, H.; Fan, L.; Shahabi, C. Differentially private H-tree. In Proceedings of the 2nd Workshop on Privacy in
Geographic Information Collection and Analysis, Bellevue, WA, USA, 3–6 November 2015.
He, X.; Cormode, G.; Machanavajjhala, A.; Procopiuc, C.M.; Srivastava, D. DPT: Differentially private
trajectory synthesis using hierarchical reference systems. Proc. VLDB Endow. 2015, 8, 1154–1165. [CrossRef]
Acs, G.; Castelluccia, C. A case study: Privacy preserving release of spatio-temporal density in Paris.
In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining, New York, NY, USA, 24–27 August 2014.
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).


Related documents


untitled pdf document 2
37i14 ijaet0514327 v6 iss2 888to902
22n13 ijaet0313536 revised
9i14 ijaet0514286 v6 iss2 639to647
37n13 ijaet0112166 revised
grad coursedescriptions researcharea


Related keywords